1. Field of the Invention
The present invention relates to a semiconductor process simulation. In particular, the present invention relates to a Monte Carlo simulation method for simulating an implanted ion distribution in a semiconductor substrate, a simulator for achieving the method, a computer program describing the method, and a semiconductor device manufacturing method including an ion implantation process based on the method.
2. Description of the Related Art
Development costs of LSIs (large-scale integrated circuits) are increasing, and to suppress the costs, improvements in the efficiency of LSI designing and development are strongly needed. The LSI designing and development need simulation techniques with quantifying capacities. Simulations required for semiconductor device design and development include a process simulation that simulates a semiconductor manufacturing process to estimate impurity distributions and element geometries in a semiconductor device and a device simulation that uses a result of the process simulation to estimate the electrical characteristics of the semiconductor device.
To simulate an ion implantation process of implanting impurity ions into a semiconductor device, a Monte Carlo simulation is frequently used. The Monte Carlo simulation approximates a two-body collision and is described in, for example, M. Posselt “Radiat. Eff. and Defects in Solids,” 130–131, 87(1994). This paper discloses a method of determining collision conditions on trial particles in a silicon crystal. This method will briefly be explained. FIG. 1A shows a unit cell contained in a silicon crystal. This unit cell is one of unit cells that are regularly arranged to form a three-dimensional space in the silicon crystal. Due to this regularity, an atom of the silicon crystal that will collide with a trial particle implanted in the silicon crystal is uniquely determinable according to the location and travelling direction of the trial particle, assuming that the thermal vibration of each atom in the silicon crystal is negligible. The unit cell of FIG. 1A is divided into basic cells such as basic cells 16 and 17 shown in FIGS. 1B and 1C having different structures, and a list of relative locations of collision candidate atoms is prepared for each basic cell. A collision candidate atom is determined according to a maximum collision parameter “pmax.” If pmax=d/2(d being a lattice constant and corresponding to a side length of the unit cell of FIG. 1A), the basic cell 16 involves 17 collision candidate atoms as depicted with black, white, and hatched circles in FIG. 2A. Similarly, the basic cell 17 involves 18 collision candidate atoms as depicted with black, white, and hatched circles in FIG. 2B.
A technique of finding collision conditions on a trial particle according to the Monte Carlo simulation will be explained. A basic cell in which the trial particle is present is found. Based on this basic cell, a list of relative locations of collision candidate atoms is obtained from a database. Thermal vibration displacements are set for the collision candidate atoms. The thermal vibration displacements, if once set, are stored without future modification because a thermal vibration speed is very slow and negligible compared with a trial particle speed.
From the obtained collision candidate atoms, a collision atom is selected. To select the collision atom, a travelling direction indicating unit vector λ of the trial particle, a relative vector x from the trial particle to a given collision candidate atom, a collision parameter p=|x x λ|, and a free-flight distance η=|x·λ| are considered. If the collision parameter p of the collision candidate atom is smaller than a maximum collision parameter pmax and if the free-flight distance η thereof is the smallest positive value, the collision candidate atom is the collision atom. In this way, a collision atom and collision conditions are obtained.
The location range of atoms to be set thermal vibration displacement, i.e., the range where collision candidate atoms are present will be explained. If a trial particle travels along basic cells that are in face-to-face contact with each other, a location range of atoms to be set thermal vibration displacement of d/2 in thickness will be defined around a basic cell in which the trial particle is present, as shown in FIG. 3. The location range of atoms 22 of FIG. 3 is orthogonal to the travelling direction of the trial particle that is in the hatched basic cell. The location range of atoms 22 is expressed as follows:(5+π)×(d/2)2≈8.14×(d/2)2
If the trial particle moves to a basic cell that is adjacent to the present cell along a single side, the range 22 is expressed as follows:(2+3×21/2+π)×(d/2)2≈9.38×(d/2)2
One problem of this technique is that it does not consider the travelling direction of the trial particle. Namely, the prior art automatically picks up, as a collision candidate atom, every atom that is within the range of a maximum collision parameter “pmax” even if the atom is not in the travelling direction of a given trial particle. The prior art has another problem that it does not consider the location of the trial particle in the basic cell. Namely, the prior art automatically sets a candidate atom picking range around a basic cell in which a trial particle is present without considering the location of the trial particle in the basic cell.
The Monte Carlo simulation examines many trial particles, and provides the distribution of the location where the particles stop. The simulation for one-dimensional structured target needs typically about 1–100 minutes. For two-dimensional simulation, the particles needs 100–10,000 times particles for one-dimension, therefore simulation time needs 100–10,000 times. For same reason, three-dimensional simulation needs further CPU time. That is, the two or three-dimensional simulation often needs several days even with the latest EWSs (engineering work station). There is a need to reduce simulation time. The present inventor recognized the fact that nearly half of a total simulation time is spent setting thermal vibration displacements and finding collision atoms and tried to reduce the number of collision candidate atoms for which thermal vibration displacements are set, to thereby minimize collision atom calculations and simulation time.